is an integer. With some abuse of notation, we also denote by \(\gamma (E)\)  the vector
\([r,d,\chi )\) , valued in \({Z}^3\)  (note the round closing bracket, to distinguish it from the vector
\([r,d,\textnormal {ch}_2]\) ). We denote the antisymmetrized Euler form byOur convention for the
antisymmetrized Euler form is consistent with
[1]}, [2]} and opposite to that in
[3]}, [4]}, [5]}, [6]}
\(\langle \gamma , \gamma ^{\prime } \rangle \chi (\gamma ,\gamma ^{\prime }) - \chi (\gamma ^{\prime },\gamma ) =3 \left( r d^{\prime }-r^{\prime } d \right)\) 
